Importing a complex SVG to Blender from Illustrator - Problems with Fill
I don't think that the intricacy  of your design is the issue here but how Illustrator is combining the many different paths. It looks like there are way too many points to create the curvature of  the paths. I suspect those extra points are the result of compunding the paths. Even in segments that are straight there are many points in a straight line.

A cure to most of the problem is converting the Handle Type to Vector


but in the areas where there are still too many control points the problem persists. Maybe there are open paths somewhere? Illustrator has tools to check for open paths.

I suspect that the paths need to be simplified and streamlined before they are exported from Illustrator to avoid the problems you are facing.